\newproblem{lay:4_1_6}{
  % Problem identification
	\begin{large}
	  \hspace{\fill}\newline
    \textbf{Lay, 4.1.6}
	\end{large}
	\\
  \ifthenelse{\boolean{identifyAuthor}}{\textit{Carlos Oscar Sorzano, Aug. 31st, 2013} \\}{}

  % Problem statement
	Determine if the set of all polynomials of the form $p(t)=a+t^2\quad \forall a\in \mathbb{R}$ are a subspace of $\mathbb{P}_2$.
}{
  % Solution
	Let $H=\{p(t)\in\mathbb{P}_2| p(t)=a+t^2\}$. We need to show that this set meets the three requirements to be a subspace
	\begin{itemize}
		\item $0\in H$ \\
		      But this is not true for $H$, there is no value of $a$ such that $p(t)=a+t^2=0\quad \forall t\in\mathbb{R}$
	\end{itemize}
	Since $H$ does not meet one of the conditions to be subspace, it cannot be a subspace of $\mathbb{P}^2$.
}
\useproblem{lay:4_1_6}
\ifthenelse{\boolean{eachProblemInOnePage}}{\newpage}{}
